PLTS TAKE OFF WITHOUT CLRNC.

Narrative

DURING AN FAA OBSERVED CHK RIDE FOR A COMPANY INITIAL CHK; WE DEPARTED ZZZ ON AN IFR FLT PLAN. AFTER BRIEFING THE DEP AND COMPLETING OUR CHKLIST; WE WERE CLRED FOR TKOF ON RWY 16L 'ACFT X CLRED FOR TKOF RWY 16L; CITATION TFC 5 MI FINAL.' I ACKNOWLEDGED CLR FOR TKOF ON RWY 16L. THEN; THE CTLR CLRED US FOR TKOF RWY 16L; NO DELAY.' WE HAD ALREADY BEGUN THE ROLL WITH PWR APPLICATION AND ACKNOWLEDGED. THE TKOF COMMENCED NORMALLY. TWR THEN CALLED US AFTER TKOF; AND WE WERE IN THE PROCESS OF EXECUTING AN AFTER TKOF ENG FAILURE (AT APPROX 600 FT AGL). I HEARD THE TWR CALL OUR NUMBER; AND I BELIEVED HE (CTLR) TOLD US TO SWITCH TO DEP. THE CHK AIRMAN ALSO THOUGHT TWR TOLD US TO SWITCH TO DEP; BUT IT WAS DURING A CRITICAL PHASE OF FLT AND WAS THE ONLY TIME COM WAS EVER NOT 100% ASSURED. WE SWITCHED OVER TO DEP AND DIDN'T FIND OUT ABOUT THE MISUNDERSTANDING UNTIL LATER. APPARENTLY; THE TWR CTLR CLAIMED HE CANCELED OUR TKOF CLRNC AT SOME POINT AFTER WE WERE CLRED FOR TKOF. MY ONLY THOUGHT IS THAT TWR MAY HAVE GIVEN US THE CANCELED TKOF CLRNC WHILE I WAS ON THE RADIO REPLYING TO HIM AND THE XMISSION COULD HAVE BEEN BLOCKED. THE FAA INSPECTOR; CHK AIRMAN AND MYSELF ALL POSITIVELY RECALL; WITH CONFIDENCE; WE DID NOT FAIL TO REPLY TO A READABLE CLRNC ON THE GND.